Random variable

A random variable turns the outcomes of a random process into numbers you can average and analyze. For example, if $X$ is the number of heads in two coin flips, then $X$ can equal 0, 1, or 2, each with its own probability. Random variables are discrete when their values are countable and continuous when they can take any value in an interval. Its long-run average is the expected value $E(X) = \sum x_i \, p_i$ (E of X, each value times its probability, summed).